Thursday, September 14, 2017

New Top Quark Width Measurement Globally Confirms Standard Model

Background

The decay width of a particle (composite or fundamental) is inversely proportional to its mean lifetime, but has units of mass-energy, rather than units of time. A large decay width implies a more ephemeral particle, while a small decay width implies a more long lived particle. Decay width also has the virtue that it can be determined directly from observation of a graph of a resonance plotted in events detected in each mass bin of an experiment.

In the Standard Model, decay width can be calculated from other properties of a particle. One first lists every possible means by which a decay of the particle is permitted in the Standard Model, then one calculates the probability per unit time of that decay occurring, then one adds up all of the possible decays.

If you omit a possible means of decay when doing the calculation, your decay width will be smaller and you will predict that the particle decays more slowly than it does in reality. If you include a decay path that does not actually occur, your decay width will be larger and you will predict that the particle decays more rapidly than it does in reality.

As a result, decay width of a heavy particle like the top quark is sensitive in a relativity robust model-independent manner to the completeness and accuracy of the Standard Model with respect to all possible particles with masses less than the top quark that it could decay into. It bounds the extent to which your model could be missing something at lower energy scales.

The top quark is the heaviest particle in the Standard Model (SM) of elementary particle physics, discovered
more than 20 years ago in 1995. Due to its large mass of around 173 GeV, the
lifetime of the top quark is extremely short. Hence, its decay width is the largest of all SM fermions.
A next-to-leading-order (NLO) calculation evaluates a decay width of Γt = 1.33 GeV for a top-quark mass
(mt) of 172.5 GeV. Variations of the parameters entering the NLO calculation, the W-boson mass,
the strong coupling constant αS, the Fermi coupling constant GF and the Cabibbo–Kobayashi–Maskawa
(CKM) matrix element Vtb, within experimental uncertainties yield an uncertainty of 6%. The recent
next-to-next-to-leading-order (NNLO) calculation predicts Γt = 1.322 GeV for mt = 172.5 GeV and
αS = 0.1181.

Any deviations from the SM prediction may hint at non-SM decay channels of the top quark or nonSM
top-quark couplings, as predicted by many beyond-the-Standard-Model (BSM) theories. The top quark
decay width can be modified by direct top-quark decays into e.g. a charged Higgs boson or via flavour-changing neutral currents and also by non-SM radiative corrections.
Furthermore, some vector-like quark models modify the |Vtb| CKM matrix element and thus Γt
.
Precise measurements of Γt can consequently restrict the parameter space of many BSM models

The last time that the top quark decay width was directly measured precisely was at Tevatron (references omitted):

A direct measurement of Γt
, based on the analysis of the top-quark invariant mass
distribution was performed at the Tevatron by the CDF Collaboration. A bound on the decay width
of 1.10 < Γt < 4.05 GeV for mt = 172.5 GeV was set at 68% confidence level. Direct measurements are
limited by the experimental resolution of the top-quark mass spectrum, and so far are significantly less
precise than indirect measurements, but avoid model-dependent assumptions.

Thus, the Tevatron one sigma margin of error was 1.475 GeV.

The New Result

The ATLAS experiment as the LHC has a new direct measurement of the top quark decay width (reference omitted):

in good agreement with the SM prediction of 1.322 GeV. A consistency check was performed by
repeating the measurement in the individual b-tag regions and confirms that the results are consistent
with the measured value. A fit based only on the observable m`b leads to a total uncertainty which is
about 0.3 GeV larger.

In comparison to the previous direct top-quark decay width measurement, the total uncertainty
of this measurement is smaller by a factor of around two. However, this result is still less precise than
indirect measurements and, thus, alternative (BSM) models discussed in Section 1 cannot be ruled out
with the current sensitivity.

The impact of the assumed top-quark mass on the decay width measurement is estimated by varying the
mass around the nominal value of mt = 172.5 GeV. Changing the top-quark mass by ±0.5 GeV leads to a
shift in the measured top-quark decay width of up to around 0.2 GeV.

Analysis

The margin of error in the ATLAS result is roughly half the margin of error of the Tevatron result.

A larger than Standard Model predicted decay width by 0.43 GeV leaves open the possibility that there could be beyond the Standard Model decay paths in top quark decays but strictly limits their magnitude, although the result is perfectly consistent with the Standard Model prediction at well under a one standard deviation level. The heavier the omitted particle, the stronger the bound from this result becomes.

The deviation above the Standard Model prediction could also result (1) from underestimation of the top quark mass (172.5 GeV is at the low end of the top quark masses that are consistent with experimental measurements), (2) from inaccuracy in the strength of the strong force coupling constant (that is only known to a several parts per thousand precision), (3) from inaccuracy in the top to bottom quark element of the CKM matrix. (The uncertainties in the W boson mass and weak force coupling constant are also relevant but are much smaller than the uncertainties in the other three quantities.)

In particular, this width measurement suggests that the 172.5 GeV mass estimate for the top quark is more likely to be too low than too high.

The result also disfavors the possibility that any Standard Model permitted decay doesn't happen, which is consistent with the fact that almost all (if not all) of the permitted Standard Model decays have almost all been observed directly, placing a lower bound on a possible decay width for the top quark.

In general, this measurement is a good, robust, indirect global test that the Standard Model as a whole is an accurate description of reality at energy scales up to the top quark mass. Any big omissions in its particle content would result in an obvious increase in the top quark's decay width that is not observed.